EXPLANATION OF CARBON IONIZATIONS
By Prof. L. Kaliambos (Natural Philosopher in New Energy) May 2, 2015 Carbon is a chemical element with symbol C and atomic number 6. However despite the enormous success of the Bohr model and the quantum mechanics of Schrodinger in explaining the principal features of the hydrogen spectrum and of other one-electron atomic systems, so far neither was able to provide a satisfactory explanation of ionizations of many electon atoms related to the chemical properties of atoms. Though such properties were modified by the periodic table initially proposed by the Russian chemist Mendeleev the reason of this subject of ionizations of elements remained obscure under the influence of the invalid theory of special relativity. (EXPERIMENTS REJECTING EINSTEIN). It is of interest to note that the discovery of the electron spin by Uhlenbeck and Goudsmit (1925) showed that the peripheral velocity of a spinning electron is greater than the speed of light which is responsible for understanding the electromagnetic interaction of two electrons of opposite spin. So it was my paper “Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures” (2008), which supplied the clue that resolved this puzzle. Under this condition we may use this image of Carbon including the correct ground state electron configuration. 1s2.2s2.2px1.2py1. According to the “Ionization energies of the elements-WIKIPEDIA” we observe that E1 = 11.26 eV, E2 = 24.38 eV, E3 = 47.8878 eV, E4 = 64.4939 eV, E5 = 392.087 eV, and E6 = 489.99334 eV. (See also my papers about the explanation of ionization energies of atoms in my FUNDAMENTAL PHYSICS CONCEPTS). EXPLANATION OF THE IONIZATION ENERGIES E1 = 11.26 eV AND E2 = 24.38 eV In my paper of 2008 I showed that the shells 2px1 and 2py1 of charge (-2e) produce deformations of the spherical shells 1s2 and 2s2, which lead to the increase of the effective ζ . ( See the paper in “User Kaliambos”). For example for a perfect screening due to spherical shells we expect to find an effective ζ = 2, because +6e -2e -2e = +2e, but the deformation of spherical shells leads to ζ >2. For calculating the first ionization energy (E1 = 11.26 eV) we must start with the second ionization energy E2 = 24.38 eV = - E(2py1) Here E(2py1) is the binding energy of the one electron with n = 2 based on the Bohr model. In this case of n = 2 we must find the effective ζ1 > 2, because the shells 1s2 and 2s2 of the charge (-4e) screen the charge (+6e ) of the nucleus. Of course for a perfect screening due to the spherical shells of 1s2 and 2s2 we should write ζ = 2. Under such a perfect condition we should write E (2py1) = (-13.6) ζ2/22 = (-13.6)22/22 = -13.6 eV However the 2py1 penetrates the 2s2 which leads to the great deformations not only of spherical shells 1s2 and 2s2 but also of 2py1. Thus writing E2 = 24.38 eV = - E(2py1) = - (- 13.6) ζ12 / 22 we get ζ12 = 7.17 and ζ1 = 2.68 > 2 . On the other hand for calculating the E1 = 11.26 eV we may write E1 = 11.26 eV = - E2 - E(2px1 + 2py1) Here E(2px1 + 2py1) = 2(-13.6)ζ22/22 is the binding energy of both electrons of 1px1 and 2py1 Since E2 = 24.38 eV we may rewrite E(2px1 + 2py1) = (-27.2)ζ22/22 = - E1 - E2 = -11.26 - 24.38 = - 35.64 eV Therefore one gets ζ22 = 5.24 and ζ2 = 2.29 Here we observe that ζ2 = 2.29 for the two electrons of 2px1 and 2py1 is smaller than the ζ1 = 2.68 of the one second electron when the first electron is absent. It means that in the absence of the first electron the symmetry breaks and leads to more deformation of spherical shells. EXPLANATION OF E3 = 47.8878 eV AND E4 = 64.4939 eV For calculating the E3 we start with the E4 = -E( 2s1). According to the quantum mechanics the one electron (2s1) penetrates the 1s2 shell. Thus it leads to greater deformations of both 1s2 and 2s1 spherical shells giving an effective ζ > 4 because the charge (- 2e) of the two electrons of 1s2 screens the charge (+6e) of nucleus. Since n = 2 we may write E4 = 64.4939 eV = -E(2s1) = - (-13.6)ζ2/22 Therefore one gets ζ2 = 18.96879 and ζ = 4.355 > 4 On the other hand for calculating the E3 = 47.8878 eV we must write E3 = 47.8878 eV = E(2s1) - (E(2s2) or E(2s2) = - 64.4939 - 47.8878 = - 112.3817 Here E(2s2) is the binding energy of the two spinning electrons of opposite spin (2s2) given by my formula of 2008: E(2s2) = + (16.95)ζ - 4.1/22 = - 112.3817 eV Then we may rewrite (27.2ζ2 - 16.95ζ + 4.1) /22 - 112.3817 = 0 Or 6.8ζ2 - 4.24ζ - 111.3817 = 0 Then solving for ζ we get ζ = 4.37 In other words we observe that the repulsions 1s2-2s1 and 1s2-2s2 give almost the same effective ζ. ' ' EXPLANATION OF Ε5 = 392.087 eV AND E6 = 489.99334 eV As in the case of the helium the ionization energy E6 = 489.99334 eV = - E(1s1) is due to the one remaining electron of 1s1 with n = 1. It should be given by applying the simple Bohr model for Z = 6 as E6 = - (-13.6057)Z2/12 = - (-13.6057)62 /12 = 489.8 eV. Surprisingly here we see that the energy of 489.8 eV given by the Bohr model is smaller than the experimental value of 489.99334 eV. It is due to the fact that after the ionizations the nuclear charge becomes greater than the electron charge of the one electron. Under this condition I suggest that the n =1 becomes n < 1. Therefore we may write E6 = 489.99334 eV = (13.6057)Z2/n2 = (13.6057)62/n2 Then solving for n we get n = 0.9998 In the same way for calculating the E5 = 392.087 eV we must apply my formula of 2008 as E5 = 392.087 eV = - E6 - E(1s2 ) = - 489.99334 - [ (-27.21)62 +(16.95)6 - 4.1] / n2 Then solving for n we get n = 0.9999 Here we see that 0.9999 > 0.9998 because the two electrons increase the electron charge with respect to the nuclear charge. 'IN THE ABSENCE OF A DETAILED KNOWLEDGE ABOUT THE SPINNING ELECTRONS OF OPPOSITE SPIN THE VARIOUS WRONG THEORIES LEAD TO COMPLICATIONS ' It is of interest to note that the E(1s2) and the E(2s2) of spinning electrons of opposite spin with n = 1 and n = 2 respectively are given by applying my formula of my paper of 2008. However In the absence of a detailed knowledge about the electromagnetic force between the two spinning electrons of opposite spin physicists today using wrong theories cannot explain the ionization energies of carbon. For example under wrong theories based on qualitative approaches many physicists believe incorrectly that the second electron of the 1s2 shell is less tightly bound because it could be interpreted as a shielding effect; the other electron partly shields the second electron from the full charge of the nucleus. Another wrong way to view the energy is to say that the repulsion of the electrons contributes a positive potential energy which partially offsets the negative potential energy contributed by the attractive electric force of the nuclear charge. Under such false ideas I published in Ind. J. Th. Phys. (2008) my paper “Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures”. Historically, despite the enormous success of the Bohr model and the quantum mechanics of the Schrodinger equation based on the well-established laws of electromagnetism in explaining the principal features of the hydrogen spectrum and of other one-electron atomic systems, so far, under the abandonment of natural laws neither was able to provide a satisfactory explanation of the two-electron atoms. In atomic physics a two-electron atom is a quantum mechanical system consisting of one nucleus with a charge Ze and just two electrons. This is the first case of many-electron systems. The first few two-electron atoms are: Z =1 : H- hydrogen anion. Z = 2 : He helium atom. Z = 3 : Li+ lithium atom anion. Z = 4 : Be2+ beryllium ion. Z = 5 : B3+ boron. Prior to the development of quantum mechanics, an atom with many electrons was portrayed like the solar system, with the electrons representing the planets circulating about the nuclear “sun”. In the solar system, the gravitational interaction between planets is quite small compared with that between any planet and the very massive sun; interplanetary interactions can, therefore, be treated as small perturbations. However, In the helium atom with two electrons, the interaction energy between the two spinning electrons and between an electron and the nucleus are almost of the same magnitude, and a perturbation approach is inapplicable. In 1925 the two young Dutch physicists Uhlenbeck and Goudsmit discovered the electron spin according to which the peripheral velocity of a spinning electron is greater than the speed of light. Since this discovery invalidates Einstein’s relativity it met much opposition by physicists including Pauli. Under the influence of Einstein’s invalid relativity physicists believed that in nature cannot exist velocities faster than the speed of light.(See my FASTER THAN LIGHT). So, great physicists like Pauli, Heisenberg, and Dirac abandoned the natural laws of electromagnetism in favor of wrong theories including qualitative approaches under an idea of symmetry properties between the two electrons of opposite spin which lead to many complications. Thus, in the “Helium atom-Wikipedia” one reads: “Unlike for hydrogen a closed form solution to the Schrodinger equation for the helium atom has not been found. However various approximations such as the Hartree-Fock method ,can be used to estimate the ground state energy and wave function of atoms”. It is of interest to note that in 1993 in Olympia of Greece I presented at the international conference “Frontiers of fundamental physics” my paper “Impact of Maxwell’s equation of displacement current on electromagnetic laws and comparison of the Maxwellian waves with our model of dipolic particles ". The conference was organized by the natural philosophers M. Barone and F. Selleri, who awarded me an award including a disc of the atomic philosopher Democritus, because in that paper I showed that LAWS AND EXPERIMENTS INVALIDATE FIELDS AND RELATIVITY. In the same period I tried to find not only the nuclear force and structure but also the coupling of two electrons under the application of the abandoned electromagnetic laws. For example in the simple photoelectric effect the absorption of light contributes not only to the increase of the electron energy but also to the increase of the electron mass, because the particles of light have mass m = hν/c2 .( See my DISCOVERY OF PHOTON MASS ).Under this condition of photon absorption an electron cannot move faster than light. However the electron spin which gives a peripheral velocity greater than the speed of light cannot be affected by the photon absorption. Thus after 10 years I published my paper "Nuclear structure is governed by the fundamental laws of electromagnetism" (2003), in which I showed not only my DISCOVERY OF NUCLEAR FORCE AND STRUCTURE but also that the peripheral velocity (u >> c) of two spinning electrons with opposite spin gives an attractive magnetic force (Fm) stronger than the electric repulsion (Fe) when the two electrons of mass m and charge (-e) are at a very short separation r < 578.8 /1015 m. Because of the antiparallel spin along the radial direction the interaction of the electron charges gives an electromagnetic force: Fem = Fe - Fm . Therefore in my research the integration for calculating the mutual Fem led to the following relation: Fem = Fe - Fm = Ke2/r2 - (Ke2/r4)(9h2/16π2m2c2) Of course for Fe = Fm one gets the equilibrium separation ro = 3h/4πmc = 578.8/1015 m. That is, for r < 578.8/1015 m the two electrons of opposite spin exert an attractive electromagnetic force, because the attractive Fm is stronger than the repulsive Fe . Here Fm is a spin-dependent force of short range. As a consequence this situation provides the physical basis for understanding the pairing of two electrons described qualitatively by the Pauli principle, which cannot be applied in the simplest case of the deuteron in nuclear physics, because the binding energy between the two spinning nucleons occurs when the spin is not opposite (S=0) but parallel (S=1). According to the experiments in the case of two electrons with antiparallel spin the presence of a very strong external magnetic field gives parallel spin (S=1) with electric and magnetic repulsions given by Fem = Fe + Fm So, according to the well-established laws of electromagnetism after a detailed analysis of paired electrons in two-electron atoms I concluded that at r < 578.8/1015 m a motional EMF produces vibrations of paired electrons. Unfortunately today many physicists in the absence of a detailed knowledge believe that the two electrons of two-electron atoms under the Coulomb repulsion between the electrons move not together as one particle but as separated particles possessing the two opposite points of the diameter of the orbit around the nucleus. In fact, the two electrons of opposite spin behave like one particle circulating about the nucleus under the rules of quantum mechanics forming two-electron orbitals in helium, beryllium etc. In my paper (2008) I showed that the positive vibration energy (Ev) described in eV depends on the Ze charge of nucleus as Ev = 16.95Z - 4.1 Of course in the absence of such a vibration energy Ev it is well-known that the ground state energy E described in eV for two orbiting electrons could be given by the Bohr model as E = (-27.2) Z2. So the combination of the energies of the Bohr model and the vibration energies due to the opposite spin of two electrons led to my discovery of the ground state energy of two-electron atoms given by E = (-27.2)Z2 + (16.95 )Z - 4.1 For example the laboratory measurement of the ionization energy of H- yields an energy of the ground state E = - 14.35 eV. In this case since Z = 1 we get E -27.2 + 16.95 - 4.1 = -14.35 eV. In the same way writing for the helium Z = 2 we get E = - 108.8 + 32.9 - 4.1 = -79.0 eV which is equal to the laboratory measurement. In the same way we can calculate the ground state energies for the Z = 3 : Li+ ion , Z = 4 : Be2+ beryllium ion, and Z = 5 : B3+ boron. The discovery of this simple formula based on the well-established laws of electromagnetism was the first fundamental equation for understanding the energies of many-electron atoms, while various theories based on qualitative symmetry properties lead to complications. Category:Fundamental physics concepts